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I knit my brows. “Hold on; that’s a little hard to follow.”

“Here. I’ll illustrate. Djuna, be a good child and get me some paper and pencil.” Djuna, who had been sitting wide-eyed and still during the whole colloquy, jumped up and eagerly supplied the requested articles. Ellery scrawled quickly on the paper for some time. Then he looked, up. “It’s impossible, as I say, to determine the angle of fire until one knows the exact position of the body at the time of the bullet’s entry. The specific cases will clarify the point. Enlargements of the film which showed the position of both victims’ torsos at the instant of impact revealed that both were leaning sideways from the saddle to the right at angles of about thirty degrees from the vertical. (It’s left from the standpoint of the victims, but right from the standpoint of the observer, or camera; I’ll call it right consistently to avoid confusion.) Now follow these diagrams.”

I rose and went to his chair. He had drawn four little pictures, which looked like this:

“The first diagram,” he said, “shows the victim’s torso in the normal erect position, as Dr. Prouty visualized it. The little arrow over the figure’s heart represents the bullet’s course in the body; Prouty said it was a downward line making a thirty-degree angle with the floor. Diagram two shows the figure still in the same position; that is, if the torso was precisely at right angles to the horse’s back; with the extension of the arrow in a dotted line to make clearer the angle of fire. The line is definitely” downward, as you see, and seems to support the conclusion that the bullet was fired from above. Well, that conclusion would be correct if the victim had been erect in the saddle, as the drawing shows him. But the victim wasn’t erect in the saddle; according to the film enlargement he was leaning to the right at an angle of thirty degrees, as the third diagram shows!

“In diagram three, then, we bend the figure to the right, as it actually was; retaining, as we must, the bullet course in the body. For, once the bullet is in the body, whether we look at the body on the floor, sitting up, bent backwards, or leaning sideways, the bullet course will always be the same in relation to the torso; if the torso swings, the bullet course swings with it; they are unchangeable elements in relation to themselves... And in diagram four we extend the line of direction from the bullet as it is lodged in the right-ward-leaning torso, and what do we find? That the line of direction, the course of the bullet, is virtually parallel to the floor! In other words, with the double’s torso and Woody’s torso (for both were approximately the same) leaning at an angle of thirty degrees to the right, the bullet wound shows a horizontal, not a downward, direction! Showing that the shot was fired not from above, but from virtually a level!”

I nodded. “And, of course, the reason Prouty said it was a downward angle of thirty degrees was that he assumed the men were riding straight as statues in the saddle. It was the thirty-degree angle of lean, so to speak, that caused the thirty-degree angle of bullet course.”

“Rather complexly put,” laughed Ellery, “but substantially correct. Now, when I knew this, I automatically ruled out two classes of suspects — and what a sweeping elimination that was! One, all those who sat in the audience, including even the first tier of seats, the boxes; for the floor of the boxes were ten feet from the floor of the arena, and anyone sitting in a box would therefore be some thirteen feet or more from the floor of the arena. A shot from this height directed at a man leaning thirty degrees sideways from a horse would have caused an even more pronounced downward angle, penetrating at more than sixty degrees, if you care for mathematics; it would have looked superficially as if the victim had been shot from the roof! And group-elimination two — the men working on the newsreel platform in the arena itself, the platform also being elevated ten feet from the level of the arena. Anyone shooting from this height would be shooting for one thing head-on rather than from the right — the head-on views of the camera prove that; and moreover the line again would be more than thirty degrees downward.

“But the line of entry was parallel to the floor, as I’ve shown. Then the murderer, in order to have been able to shoot a horseman in the breast on a line parallel to the floor, must himself have been a horseman! Do you follow that?”

“I’m not an idiot,” I retorted.

He grinned. “Don’t be so sensitive. I’m not quite sure it’s immediately understandable. Yet it’s a clear-cut deduction. Had the murderer been standing on the floor of the arena, the course of the bullet would have shown a slight upward direction. Had the murderer been in the audience the course of the bullet would have shown a sharp downward direction. So for the bullet to enter the victim’s body on a perfectly straight line the murderer must, as I’ve said, be at the same height from the floor as the victim, and shooting on a straight line, too. But since the victim was a horseman, the murderer must have been a horseman, too, shooting with his pistol raised to the level of his own heart.

“The only logical suspects, then, I saw at once, were the horsemen in the arena, the troupe of riders following the victim in each instance. There was one other person on horseback besides the troupe: Wild Bill Grant. But Grant couldn’t possibly have fired the shots; both times he was in the exact center of the arena at the time of the murder. The camera snapped the victims head-on, which meant that the shots, which pierced the victims’ bodies from the right, must have been fired from the specific direction of the Mars box, nearly at right angles to the victims. But Grant was virtually facing the victims, like the cameras. Grant, then, couldn’t have fired the shots. But the entire troupe was directly under the Mars box at the instant the shots were fired; this checked with my deduction about a horseman having been the murderer. From the standpoints of direction and angle of entry I could now make the positive assertion.”

“I see that, all right,” I said, “but what I can’t understand is why you permitted twenty thousand innocent people to go through the embarrassment and annoyance of being detained and searched for the weapon, when you knew perfectly well not one of them could be the murderer.”

Ellery squinted quizzically at the flames. “There you go, J.J., falling into the common error of confusing, definitions. The carrier of the weapon wasn’t necessarily the murderer. There are such creatures as accomplices, you know. It would have been relatively simple, in the confusion following both murders, for one of the suspect horsemen to have thrown the weapon to some spectator in the audience — over the rail above his head. And, of course, it was imperative that we find the murder weapon. Ergo, the heroic measure.

“Now, if the murderer was one of the riders in the arena, then Horne — on the hypothesis that he was the murderer — must have been acting as a member of the troupe! Now how could he have been? Simply enough. I said to myself: Naturally he isn’t Buck Horne now, but someone else. He’s made up, disguised. Not at all a difficult task for an ex-actor. What did Horne look like? I knew he had white hair. Obviously, then, if he wanted to disguise himself, he would dye his hair. Then by a change of costume, slight alterations of posture, walk, voice, he could easily have deceived people who had known him as Buck Horne only superficially. And then, too, observe the cleverness of his psychological action in assuming a hideous scar. A mutilation like that catches all the attention, for one thing, and tends to make people neglect the other features; and then too, as I saw myself, people’s tendency is to avoid looking at a mutilated face for fear of giving offense to the unfortunate afflicted. I rather applaud Horne’s shrewdness there.”